Question

Asked Sep 19, 2019

Define the following with an example

(a) random experiment

(b) sample space

(c) events

(d) independent events

Step 1

**a.**

*Random Experiment:*

Random experiment is the experiment which is conducted under identical conditions and results of the experiment are different from trail to trail.

Example:

Tossing a fair coin and selecting a card from the deck of 52 cards.

Step 2

**b .**

*Sample space:*

The sample space is the collection of all outcomes, if a random experiment is performed.

In this case, the random experiment involves tossing 3 fair coins. While writing out the sample space, we shall consider the order; for example, if the first coin shows head, the second coin shows tail and the third coin again shows head, we shall write it as “hth”, according to the notation you have given.

Keeping these in mind, the sample space is: {hhh, hht, hth, htt, thh, tht, tth, ttt}.

Step 3

**c.**

*Events:*

The outcomes of the experiment are known as events and the set of outcomes are known as sample space.

Example:

Consider the experiment of throwing a die. The outcomes of the experiment are

Define the event as,

*A*: Getting a prime number ...

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